for the "normal" scenario of one file == one package;
is there ever a case where our (instead of my) is needed?

Needed? You need a global variable if you are going to set one with special meaning to Perl, or to an external module. But even then you don't need our to set those globals. (The most common globals that people do this with are @ISA, $VERSION, @EXPORT and @EXPORT_OK.)

For instance a lot of people tend to write:

package Foo;
use strict;
our @ISA = 'Bar';
...
[download]

instead of

package Foo;
use strict;
use vars qw(ISA);
@ISA = 'Bar';
...
[download]

so you can save a line. However you can solve that problem in other ways, for instance:

package Foo;
@ISA = 'Bar';
use strict;
...
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or

package Foo;
use strict;
@Foo::ISA = 'Bar';
...
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or in this case

package Foo;
use strict;
use base 'Bar';
...
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So our is always pretty gratuitous.

If you want a global variable, i.e. one that can be read from other packages and does not go out of scope, then you either spell the whole thing out ($SomePackage::Variable) or use our so you can say ($Variable) within that file.